Surveyors in ancient Egypt had a simple tool for
making near-perfect right triangles: a loop of rope divided by knots
into twelve equal sections. When they stretched the rope to make a
triangle whose sides were in the ratio 3:4:5, they knew the largest
angle was a right angle.

Can you fit the five pieces at bottom into the two smaller squares
above the right triangle? Then can you fit the same five pieces into
the larger square below the right triangle? If you can do both, what
have you done?